(Regression analysis) How can I correct for omitted variable bias in this case?
Let's suppose I just want to run two regressions:
Y = b0 + b1x1
Y = b0 + b1x1 + b2x2
The idea here is that I want to see what happens to b1 when I include x2 into the regression. The problem is, I know that there is a third factor (which I can easily measure) which affects both x2 and Y. Therefore, including x2 without x3 will lead to a bias.
The catch is, I do not want to include x3. I just want to know what happens to b1 after including x2. Is anybody aware of any method in which I can accomplish this? For example, I imagine there might be a way to condition my values of x2 on values of x3 and include that in the second regression. Thanks so much!
Re: (Regression analysis) How can I correct for omitted variable bias in this case?
You might want to consider using a non-linear general regression model where you specify the distributions of each variable and its constraints.
In SAS there is a procedure called NLMIXED that does this and there are also MCMC techniques.
I'd suggest taking a look at NLMIXED if you can (in SAS) and see if you can specify all of the constraints explicitly so that you can get estimates for the regression co-efficients given both models (along with standard errors).